Relaxed Conditions for Parameterized Linear Matrix Inequality in the Form of Double Fuzzy Summation

The aim of this study is to investigate less conservative conditions for a parameterized linear matrix inequality (PLMI) expressed in the form of a double convex sum. This type of PLMI frequently appears in Takagi–Sugeno (T–S) fuzzy control system analysis and design problems. In this letter, we derive new less conservative linear matrix inequalities (LMIs) for the PLMI by employing the proposed sum relaxation method based on Young's inequality. The derived LMIs are proven to be less conservative than the existing conditions related to this topic in the literature. The proposed technique is applicable to various stability analysis and control design problems for T–S fuzzy systems, which are formulated as solving the PLMIs in the form of a double convex sum. Furthermore, examples are provided to illustrate the reduced conservatism of the derived LMIs.